Valerie Lucus-McEwen has a very good article in the current edition of Emergency Management Magazine, see Dueling Degrees: Emergency Management vs. Homeland Security
This is written from an academic's perspective with much of the piece articulating the differences that sprung up after the Terrorist Attacks of 9/11 when many organizations, not just colleges and universities, jumped on the Homeland Security bandwagon when they saw dollars getting ready to flow to anything and anyone with that moniker.
During the course of the article it is implied that emergency management degrees are for state and local folks and homeland security degrees are for those who are more concerned with national affairs. I can tell you this, if you are looking for a job working in the profession of emergency management you will need to be a practitioner and also know what is going on at the national level in order to follow the "bouncing legislative and policy ball." I suppose that if you are pursuing an advanced degree the differences might be more pronounced because of your specialization. But, day-to-day we are all in the trenches together.
This debate about homeland security and emergency management reminds me of the old argument from long ago How Many Angels can Dance on a Pin? Who cares? What difference does it make to me and my life? Since the academics have to spend their time doing something, why not argue about the differences between to very related topics that are combined from the Federal Emergency Management Agency (FEMA) on down.
I think that those states that established separate homeland security offices made a huge mistake. They lost the integration with what emergency management needed to be doing everyday and led to much duplication and wasting of resources. California is one state that corrected this situation a few years back and combined the two separate functions into one office.
Lastly, there are those who cannot be accused of jumping on the latest fad. You can spot them by the names of their organizations that remain tied to civil defense. Now there is a name that might be ripe for changing and being updated to reflect 21st century realities of emergency management.